Everyone in SCASD seems to agree that we need a “balanced” math program. The problem is that there are different ideas of what “balance” means. In my view, the most important balance that needs to be struck is between strict constructivism (the idea that children should construct their own math knowledge with a teacher serving as a facilitator) and direct instruction (which has teachers and texts showing students how to solve problems followed by student practice).
This guy seems to me to be an excellent teacher who has found a great way to balance these approaches:
Dan Meyer is a young high school math teacher in Santa Cruz, CA, who has found creative ways to interest students in math through the use of “real life” examples and who strongly believes that highly structured problems in math textbooks are unhelpful.
In the above video, he sounds like a teacher who would prefer a strict constructivist approach like that employed in Investigations, but that turns out not to be the case. On his blog, Mr. Meyer makes it clear that the benefits of strict constructivism are outweighed by the inefficiency that comes with it. He prefers to follow up his examples with direct instruction:
I have to take great pains to point out to skeptical teachers that, even though you’re investing extra time on these kind of investigations, that investment into rigorous mathematical thought processes pays off huge dividends in direct instruction where you find students less impatient, more tenacious, and quicker to learn new skills by evaluating them against their existing intuition.
In a perfect world with unlimited time, he might like to stick with constructivism, but in this world Mr. Meyer believes that his use of direct instruction along with examples that appeal to students’ intuition results in a time savings of 75%:
I have determined my constructivism multiplier to be four, which is to say it takes me four times longer to bring a student to conceptual understanding through conversation and questioning in a social situation the student helped create than it does to get up in front of the class and simply give it to them straight, no chaser, through direct instruction and a handout of questions I wrote.
What I find maddening about conversations with committed constructivists (cf. the conversation here) is the reflexive assumption that educators choose direct instruction because they’re either power-drunk or self-obsessed or because they lack faith, courage, or high expectations. I can’t, personally, wave so dismissively at the massive institutional impediments to student-constructed learning.
My district in WA uses the mantra “balanced math” as an excuse to continue using the extremely unbalanced Investigations curriculum. They even hired an expensive consultant from Colorado, who wrote a book called “5 Easy Steps to a Balanced Math Program”.
Unfortunately teachers have to develop all the material for each of the five steps. As a result most teachers simply grab their Investigations materials because it’s more efficient to use already prepared lessons.
The very notion that we should try to “balance” Investigations has cost our district hundreds of thousands of dollars in consulting fees, and our math scores continue to decline. What we really need is a world-class math curriculum that is already balanced. We are wasting valuable money and time trying to support TERC, when we should have replaced it years ago.